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Quantitative Analysis of grafted CNT dispersion and oftheir stiffening of polyurethane (PU)

M. H. Jomaa, Lucian Roiban, D. S. Dhungana, J. Xiao, J.y. Cavaillé, L.Seveyrat, L Lebrun, G. Diguet, Karine Masenelli-Varlot

To cite this version:M. H. Jomaa, Lucian Roiban, D. S. Dhungana, J. Xiao, J.y. Cavaillé, et al.. Quantitative Analysisof grafted CNT dispersion and of their stiffening of polyurethane (PU). Composites Science andTechnology, Elsevier, 2019, 171, pp.103-110. �10.1016/j.compscitech.2018.12.012�. �hal-02156618�

1

Quantitative Analysis of grafted CNT dispersion and of their

stiffening of polyurethane (PU)

M. H. Jomaaa,d, L. Roibana*, D. S. Dhunganaa,e, J. Xiaoa, J.Y. Cavailléa,b, L. Seveyratc, L.

Lebrunc, G. Diguetb, K. Masenelli-Varlota*.

a Univ. Lyon, INSA-Lyon, Université Claude Bernard Lyon 1, MATEIS, UMR 5510, CNRS, 7

avenue Jean Capelle, F-69621 Villeurbanne Cedex, France

b ELyTMaX, UMI 3757, CNRS, Tohoku University and Université de Lyon, International Joint

Unit, Tohoku University, Room#503, MaSC Building, Katahira 2-1-1, Aoba-Ku, Sendai, 980-

8577, Japan

c Univ Lyon, INSA-Lyon, LGEF, F-69621 Villeurbanne cedex, France

d Current location: Queen’s University Belfast, Queen’s Advanced Micro Engineering Centre,

Belfast, BT9 5AH, UK

e Current location: CNRS, CNRS-LAAS, University of Toulouse, 7 Avenue du Colonel Roche,

F-31400 Toulouse, France

* Corresponding authors: MATEIS, bâtiment B. Pascal, 7 avenue J. Capelle, 69621

Villeurbanne cedex, France. Lucian.Roiban@insa-lyon.fr ; Karine.Masenelli-Varlot@insa-

lyon.fr

Abstract

Electroactive devices are developed for energy conversion purposes. In particular,

polyurethanes (PU) are lightweight and flexible materials, which have demonstrated their

ability to convert electrical energy into mechanical energy (actuation by electrostriction) and

vice-versa (energy harvesting). It has been shown that energy conversion efficiency can be

increased by incorporating carbon nanotubes (CNTs) into a PU matrix. The counterpart of this

2

improvement is the stiffness increase, which in turn limits the electrostriction efficiency. On the

other hand, it is well known that CNTs are hardly dispersed in a polymeric matrix, and that the

interfacial adhesion strength is generally poor. One solution to improve both dispersion and

adhesion consists in grafting polymeric chains onto the CNT surfaces. As most of the works

dedicated to improve material electroactivity are mainly empirical, this work aims to (i) better

characterize these material microstructures by electron tomography, through the measurement

of the CNT tortuosity, the CNT-CNT minimum distance and the number of their contacts, and

(ii) and to predict their mechanical stiffness from these microstructural data. From electron

microscopy observations of the studied materials, CNTs can be assumed to be composed of

successive stiff rods of measured length and orientation, linked together by flexible kinks. Their

mechanical stiffening effect in PU is, simply and in an original way, evaluated using the

classical analytical equations derived by Halpin and Kardos, accounting for the microstructural

parameters determined by electron tomography. It appears clearly that, due to their tortuosity

and despite their ultra-high longitudinal stiffness, CNTs only poorly stiffen soft matrices. Fully

stretching 10 m long nanotubes increases the composite modulus by almost 10 for a fraction

of only 2 vol.%.

Keywords: carbon nanotubes; polymers; smart materials; scanning/transmission electron

microscopy (STEM); mechanical properties

1 Introduction

The last developments in electroactive materials (EAP) show promising properties especially

for actuation and energy harvesting applications. Compared to inorganic materials, these

versatile polymers have various attractive properties, such as being lightweight, inexpensive

and easy to manufacture. A tremendous amount of research and development has proved that

EAPs can change their size or their shape when stimulated by an external electric field, meaning

3

they can convert electrical energy into mechanical energy. Among the various EAPs,

polyurethane (PU) elastomers are of great interest due to their significant electroactivity [1]

combined with flexibility, high mechanical strength and biocompatibility with blood and tissues

[2,3]. In addition, it has been shown that the incorporation of nanofillers, such as carbon

nanotubes (CNTs), into PU matrices can also enhance their electromechanical properties [4].

However, CNTs are difficult to disperse in a polymeric matrix and it is worthy to notice that

the CNT-matrix interfacial adhesion strength is generally poor [5]. Furthermore, in composite

materials and especially in nanocomposites, the improvement of the materials

electromechanical performance is generally related to (i) the dispersion, (ii) the interaction of

nanotubes with the host polymer (interfacial adhesion strength), and (iii) the alignment and

orientation of the nanotubes in the polymer matrix [6]. One solution to improve both dispersion

and adhesion consists in functionalizing CNTs by grafting polymer chains onto their surfaces

[7, 8].

In order to highlight the effect of grafting on the dispersion of CNTs in polyurethanes, several

parameters have to be precisely determined, such as the distance between CNTs, the number of

the contacts between them, their orientation, their curvature as well as the distance between

entanglements/contacts. Measuring such parameters requires a three-dimensional

characterization. Electron tomography is undoubtedly the most pertinent technique able to

perform a three-dimensional analysis of polymer / CNT microstructures. Few electron

tomography studies dealt with the characterization of polymer / CNT nanocomposites [9, 10,11,

12, 13]. To our knowledge, only Natarajan et al. [14] reported a quantitative analysis of the

tomograms and related the evolution of several morphological parameters with the CNT volume

fraction in epoxy-based nanocomposites. Alternatively, 2D images have been used to quantify

the CNT orientation [15, 16] or the mean distance between neighboring CNTs [17]. Although

4

they could provide nice agreements with experimental data, the methods used could contain

artifacts due to the use of 2D projections of a 3D volume.

The aim of this work is to analyze the effect of CNTs and their grafting onto the actuation

properties of PU. For this purpose, we first quantify several structural parameters. In a second

step, we predict their mechanical stiffness from the microstructural data obtained by electron

tomography. It appears clearly that, due to their tortuosity and despite their ultra-high

longitudinal stiffness, CNTs only poorly stiffen soft matrices.

2 Materials and methods

Films composed of a polyether-based thermoplastic polyurethane (Estane 58888 NAT021 –

Lubrizol) and either grafted or non grafted multi-walled carbon nanotubes (CNT) (from Cheap

Tubes Inc.) were prepared by solution casting according to a procedure described elsewhere

[18]. Briefly, CNTs had an average diameter of 30 nm and lengths ranging between 10 and 20

µm. A “grafting onto” technique was used to graft PU chains onto CNTs [19]. Figure 1(a) and

(b) show typical Transmission Electron Microscopy (TEM) images of as-received CNTs and

grafted CNTs, respectively.

a)

b)

5 nm 5 nm

5

Figure 1: TEM images of the CNTs a) before any treatment and b) with PU chains grafted

onto the sidewalls, forming a thin amorphous layer.

The polymer films were prepared by a solution casting method. Before use, PU granules were

heated at 350 K for 3 hours. The grafted CNTs were first dispersed in N,N-dimethylformamide

(DMF, Sigma-Aldrich D158550, 99 %) using sonication in an ultrasonic bath (Bioblock

Scientific TS540 (power 10 %)) and /or using an ultrasonic processor with a 7 mm sonotrode

(Hielscher UP400S 400 W, 24 kHz, (power 30 %)). PU granules were added to this solution

with a ratio of 15 wt.% of PU into DMF. The solution was heated at 350 K for 4 hours under

mechanical agitation, until a homogeneous solution was obtained. This operation was carried

out in a closed device, to avoid evaporation of DMF and to ensure good reproducibility of films.

Then, the solution was kept overnight to remove air bubbles. Afterwards, this solution was cast

on glass plates with an Elcometer 3700 Doctor Blade ® film applicator, put in an oven at 335

K for one day, and then removed from the glass. A second heating treatment at a temperature

below the HS melting temperature was performed at 400 K for 3 h in order to eliminate any

residual solvent. The final thickness of the films was measured to be about 100 µm after drying.

In the following, the blade displacement will be referred as "Machine direction" or Md. The

normal direction (Nd) is perpendicular to the film, while the transverse one (Td) is in the film,

perpendicular to Md. The directions are schematically represented in Figure 2 (a).

Two samples composed of PU with 2 wt.% of either grafted or ungrafted CNTs were prepared

for electron tomography analysis. The specimens were embedded in epoxy and microtomed at

low temperature (T = 200 K) with a Reichert Ultracut S cryo-ultramicrotome equipped with a

35° diamond knife (knife speed set to 1 mm/s, knife movement 100 nm). The cutting was

perpendicular to Md, i.e. in the (Nd, Td) plan, along the Nd direction; Figure 2 (b) gives a

schematic representation of the film orientation during ultramicrotomy. Ultrathin sections were

6

deposited on a copper grid covered with a holey carbon film. Gold nanoparticles of a diameter

of 15 nm were deposited on the surface of the thin sections. They were used to enhance the

contrast during acquisition and to facilitate the alignment of the projections after the tilt series

acquisition.

a)

b)

Figure 2: Definition of the sample orientation and corresponding frames. a) Schematic

representation of the elaboration process with the directions Md, Td and Nd . A schematic

representation of the electron tomography set-up for environmental SEM is given with the

tomography referential (x,y,z) showing that z-axis is the Md direction. b) Low resolution

image of an ultramicrotomy thin section with the Nd and Td directions reported to the x,y,z

directions used in electron tomography. The white spots are Au nanoparticles.

Tilt series were acquired with a FEI XL-30 FEG environmental scanning electron microscope

(ESEM) operating at 30 kV under 400 Pa of water partial pressure. The environmental mode

Y

XZ

130°

7

allows a gas flow having the capacity to drive out the charges, thus facilitating the study of non-

conductive samples. The sample was placed on a home-made holder allowing a high tilt angle

[20]. A solid detector placed 10 mm below the sample was used to collect the electrons scattered

between 14° and 40°. The contrast obtained in the recorded images is mass-dependent [21]. The

ESEM performances combined with the chosen imaging mode push the resolution down to a

few nm [22], including in three dimensions [20]. Tilt series were acquired with angles ranging

from +66° to -66°, with a constant tilt step of 2°. Prior to the acquisition, the stage and the

samples were cleaned in situ using an Evactron system to avoid contamination during the tilt

series acquisition. Moreover, the region of interest was irradiated during 5 minutes with the

electron beam to avoid shrinkage problems during acquisition. Although this is known to induce

chemical changes inside the polymeric phase, it is thought not to affect the CNT distribution.

In electron tomography, the axes (x, y, z) are defined, where z represents the direction of the

sample depth, x and y being the horizontal and vertical axes in the image. From the geometry

used in cryo-ultramicrotomy, it is obvious that z corresponds to Md. The relation between (x,

y) and (Md, Td) is given by linear defects in the sample, visible at low magnification (see Figure

1 (b)). These defects can be attributed to scratches introduced by the diamond knife during cryo-

ultramicrotomy. Therefore, the linear defects correspond to the cutting direction, Nd. In the film

containing grafted CNTs, the angle between Nd and x is measured to be equal to +130° (or

310°) and the angle between Td and x is thus equal to 40° (or 220°).

After the tilt series acquisition, an accurate alignment of the projections is performed in

ETOMO, using gold nanoparticles as fiducial markers [23]. The volume reconstruction is done

using the TomoJ [24] plugin of ImageJ software, with the ART algorithm (15 iterations). The

ART reconstruction algorithm is an iterative algorithm that projects the reconstructed volume

and compares one by one the calculated projections with the original ones. The difference

between projections is projected until both a chosen number of iterations and convergence are

8

reached [25]. Other reconstruction algorithms can be found in the literature and have been

compared in the literature [26], [27], [28]. In the present study, we preferred to use ART, as it

allows a better preservation of the reconstructed object shape after correction by the elongation

factor. However, segmentation is more time-consuming with ART as the reconstructed volume

is noisy. Segmentation is carried out combining Trainable Waka Segmentation [29], with other

plug-ins [30] in Fiji, and 3D Slicer (http://www.slicer.org/) [31], further used for advanced

segmentation.

3 Results and discussion

Figure 3 a) and b) show orthogonal cross-sections extracted from the reconstructed volumes,

in the case of nanocomposites containing grafted and ungrafted CNTs, respectively. The white

dots are the gold nanoparticles. The contrast allows identifying the CNT distribution within

the PU matrix. From the volume analysis at different depths and orientations, the thicknesses

of the analyzed samples are measured to be around 350 nm and 450 nm for the nanocomposites

containing grafted and ungrafted CNTs, respectively. The dispersion of grafted CNTs is found

to be rather uniform and only small heterogeneities are observed within the analyzed volume,

whereas in the sample containing ungrafted CNTs, regions with different densities of CNT are

observed. Grafting CNTs seems to improve the CNT dispersion within the PU matrix. This is

consistent with the impressive improvement of the stability of the CNT suspension in DMF

upon grafting [18]. The interfacial adhesion strength is also expected to be excellent since the

same chemical component is present in both sides of the interfaces (PU in the grafted layer

and in the matrix).

9

3.1 Quantification and control of the CNT dispersion state

The volume quantification is carried out considering two main objectives: (i) characterization

of the CNT dispersion state and (ii) measurement of the CNT orientation state. To facilitate

these objectives, virtual markers are numerically placed in the three-dimensional model

obtained by segmentation of the reconstructed volume. The positions of the markers are

considered in order to obtain clear statistical information of possible contacts between the CNTs

within the sample.

Each CNT being considered as a polyline, the virtual markers are placed manually at the

endpoints where a change in the direction of the CNT is observed. Then, the spherical

coordinates of the virtual markers are extracted (see Figure 4 a)). Two consecutive markers

define a segment and one CNT is composed of a variable number of segments having different

orientations. From the markers coordinates, each CNT segment is then characterized by its

length r, polar angle 𝜃 (representing the segment orientation with respect to the z axis), and

azimuthal angle (representing the segment orientation in the x,y plane, with respect to the x

axis). Analyzing the segment positions and orientations give rise to a direct measurement of the

CNT dispersion and orientation within the PU matrix.

a)

xy xz

10

b)

c) d)

Figure 3: Orthogonal cross-sections through the reconstructed volumes of the samples:

a) with grafted CNTs, b) with ungrafted CNTs. The red dashed lines show the intersection

between the orthogonal slices. c) and d) three-dimensional models obtained after

segmentation, with grafted CNTs in blue and ungrafted CNTs in green.

a)

xy xz

Dispersion of CNT Orientation of CNT

Distance between CNT (di)

x

z

y

q

ϕ

(Z)

A1(r1, ϕ1, q1)

A2(r2, ϕ2, q2)

An(rn, ϕn, qn)

Length of a CNT Segment

11

b)

-90 -60 -30 0 30 60 900

10

20

30

40

CNT orientation in Y,Z plane

Polar angle q(°)

Num

ber

of segm

ents

c)

-180 -90 0 90 1800

5

10

15

CNT orientation in X,Y plane

Azimuthal angle (°)

Num

ber

of segm

ents

Figure 4: Characterization of the CNT dispersion and orientation: a) Schematic

representation of the quantification method used for the analysis of the CNT orientation. b)

CNT orientation for the grafted sample (with 2 % of CNTs), the polar angle θ representing

the orientation of each segment in the YZ plane. c) CNT orientation for the grafted sample,

the azimuthal angle φ representing the orientation of each segment in the x,y plane.

The quantitative parameters describing the CNT dispersion state are shown in Table 1. The

minimum distances between CNTs are measured using the segment method applied on the

three-dimensional model. The average length of the segments slightly increases from ungrafted

to grafted containing 2 vol.% of CNTs suggesting that the grafted molecules help to rigidify the

CNTs. The further increase, observed from 2 vol.% to 4 vol.% of grafted CNTs, might rather

be a dispersion-related phenomenon, such as bundles formation, for instance. The values

obtained confirm that grafted CNTs are not in direct contact with each other in the

nanocomposites containing 2 vol.% of grafted CNTs and a minimum distance around 50 nm is

obtained. On the contrary with 2 vol.% of ungrafted CNTs and 4 vol.% of grafted CNTs, 11

and 5 contacts between CNTs have been found within the analyzed volumes, respectively. The

formation of percolating paths may reflect overall conductive materials. This suggests that for

2 vol.% of CNTs, grafted CNTs are better dispersed than ungrafted CNTs. Moreover, the

percolation threshold seems to be close to 4 vol.% of grafted CNTs. This is in very good

agreement with macroscopic electrical measurements, where the percolation threshold was

12

found to lie between 4 and 5 vol.% on the same films [18]. In the following, only grafted CNTs

will be considered.

Table 1: CNT distribution within the volume of PU: analyzed volume, number of contacts

between the CNTs counted in the total analyzed volume, and minimum distance between CNTs

reported to the matrix volume. The mean length of the CNT segments is also given.

Type of

Composite

Mean length

of CNT

segments

Number of

Contacts

Minimum

Distance

Analyzed

volume

Ungrafted

CNTs

(2 vol.%)

500 nm 11 0 7.520 µm3

Grafted CNTs

(2 vol.%)

590 nm 0 ≈ 50 nm 7.550 µm3

Grafted CNTs

(4 vol.%)

800 nm 5 0 6.600 µm3

For PU grafted with 2% of CNTs, the polar angles θ follow a Gaussian distribution centered

near θ ~ 0° (Figure 4 b)), i.e. the Md direction. The azimuthal angle distribution is bimodal,

with two preferential orientations at 130° and 310° (Figure 4 (c)). These supplementary

angles actually represent the same CNT planar direction and this was previously identified to

the cutting direction for cryo-ultramicrotomy, hence it corresponds to the direction Nd. The

preferential values of q and clearly indicate that the CNTs were in the film plane. Moreover,

the CNT orientation state in the (Md, Td) place can be deduced from the values of q and .

When projecting a CNT segment onto the (Md, Td) plane, it is possible to define an angle in

13

this plane, , between the projected segment and the Md axis. Using geometrical considerations,

it can be shown that

𝑡𝑎𝑛(𝛽) = 𝑡𝑎𝑛(𝜃). 𝑐𝑜𝑠(𝜑 − 40°)

-90 -60 -30 0 30 60 900

10

20

30

40

50

60

Nu

mb

er

of

se

gm

en

ts

Angle (°)

CNT orientation in the (Md, Td) plane

Figure 5: CNT orientation in the (Md, Td) plane, for the sample containing 2 vol.% of

grafted CNTs. The angle represents the angle between a CNT segment and the Md axis.

The distribution of angles indicates that the CNTs are rather well oriented along the Md

direction (see Figure 5). The appearance of a preferential orientation has already been observed

in the literature. For example, Ma et al. [32] used an electric field to align pristine or

functionalized MWCNTs. Xie et al. [33] reviewed studies related to alignment of CNTs in a

matrix, especially using force and magnetic fields, electrospinning and procedures involving

liquid crystals. More recently, K. Gnanasekaran et al. [15] quantified TEM images of spin-

coated latex/CNT composite films and could evidence CNT alignment along the spin-coating

direction, providing that the measurements are carried out on large enough areas. In our case,

the film was cast on glass using a Doctor Blade Film Applicator. This technique does not give

rise to intense shear and no external force or electric field is applied but an anisotropic

orientation state is already obtained.

14

3.2 Evaluation of mechanical stiffening of PU by CNTs

The main purpose of this section is to evaluate if it is possible to relate the parameters found

from the 3D analysis, presented above, with the stiffening observed by mechanical

measurements. There are few cases where the problem of stiffening effect can be evaluated with

analytical equations as, in most cases, an accurate evaluation requires the use of numerical

simulations often based on finite element calculations. The rare cases where analytical

equations can be powerful and lead to rather accurate predictions concern (i) spherical or

ellipsoidal particles [34, 35] and (ii) short stiff particles or rods. For instance, Halpin and Tsai

[36] and Halpin and Kardos [37] proposed equations where not only the shape factor of the

particles (i.e. their length divided by their diameter) but also their elastic constant anisotropy

might be considered.

However, for the case where particles are in fact flexible short fibers, like CNTs, it is extremely

difficult to model the composite mechanical properties. J. Pascual et al. [38] found

discrepancies between experimental elastic modulus values and the Halpin-Tsai model. They

attributed the differences to the presence of CNT aggregates but the CNT waviness was not

discussed. Yet, it is well known that the curvature (bending) of fibers decreases drastically their

stiffening effect [39], compared to straight fibers especially when the stress is mainly applied

parallel to the fiber axis. The effect of the CNT waviness on the thermal properties of

polycarbonate/CNT composites has, for instance, been evidenced and modeled by Yu et al.

[40]. The model was also modified to take into account randomly oriented fillers [41] or by

introducing a “waviness ratio” [42, 43] or an "orientation factor" [44], both parameters being

unfortunately not experimentally measurable.

As there is no way to model the exact microstructure of these nanocomposites, and in order to

relate the stiffening induced by the nanotubes to their parameters given in Table 1, we assume

in the following that CNTs consist in a series of stiff rods linked together by flexible joints. As

15

the CNT flexibility is very high compared to their longitudinal compliance and again because

there is no way to go deeper in this analysis, it will be assumed that the main stiffening effect

comes from the stress transfer from the matrix to the CNT segments. This means that the knees

(junctions between two segments) are assumed to transmit no moment from a segment to the

adjacent one. From previous studies on composite materials stiffened by perfectly straight

cellulose nanocrystals [45], the effect of the stiffness of contacts between the cellulose rods was

quantified. Depending on the process, these contacts are very strong when hydrogen bonds are

formed between nanocrystals, or very weak if hydrogen bonds are not allowed to form [46].

The composite stiffness differs by almost 3 decades for 5 vol.% of cellulose whiskers if contacts

are stiff or not. If we agree that the knees play almost no role, the situation is close to the one

where straight segments are randomly dispersed in the matrix. In the present case, such

assumption gives a unique opportunity to evaluate the effect of CNTs on the mechanical

properties of the composites with a model fully based on the composite structure and on the

characteristics of each component, i.e. without any adjustable parameter.

As a first attempt, we consider in the following that in the materials studied here, each CNT can

be considered as a set of stiff straight rods independent to each other, as far as deformation is

very small. The main stiffening mechanism consists in stress transfer from the matrix towards

these rods, while the flexible joints play almost no role.

The components of the elastic constant tensor can be written as:

Eii

Gm

=2E

f ii(1+n

m)(1+x

iiX

f)+4x

ii(1+n

m)2(1- X

f)G

m

Ef ii

(1- Xf)+2(x

ii+ X

f)(1+n

m)G

m

(1)

where refers to the longitudinal composite modulus (direction i), refers to the fiber

longitudinal modulus, refers to the isotropic matrix shear modulus, to the matrix Poisson

E

ii E

f ii

G

m n

m

16

ratio, , the fiber volume fraction and

x11

= 2L

e

æ

èçö

ø÷,

x12

=l

e

æ

èçö

ø÷

3

,

x22

= 2l

e

æ

èçö

ø÷, with L, l and e,

the length, thickness and width of the rods.

The composite shear modulus is given by:

G =E

11+ E

22(1-n

12)

8(1-n12n

21)

+G

12

2 (2)

where n

12= X

fn

f+(1- X

f)n

m, and

n

12=n

21

and,

G12

Gm

=G

f(1+x

12X

f)+x

12(1- X

f)G

m

Gf(1- X

f)+(x

ii+ X

f)G

m

(3)

From Equ.2, using the complex expression of the mechanical moduli to account for the matrix

viscoelasticity ( ' "m m mG G iG ), it is then possible to calculate the composite shear modulus, in

which "'G G iG . Within the temperature range considered in this study, the CNT elastic

constants (here Gf) remain almost temperature-independent so that the composite shear modulus

can be calculated for all temperatures using for the matrix modulus Gm, available from

experimental measurements. In Figure 6, the real part of the composite shear modulus G' is

plotted against temperature at constant frequency of 0.1 Hz; the measurements are made with

an inversed torsion modulus described in literature [47]. As the stiffening effect is mainly

effective when the matrix is soft, the shear modulus is normalized at 1 GPa at 150 K. The main

reason is that torsional measurements are very accurate to detect relative changes. However,

they cannot really provide absolute values: the measured modulus requires the knowledge of a

geometrical parameter, which depends on the cube of the sample thickness, leading to a large

uncertainty just because of sample dimension irregularity due to their preparation.

X

f

G

17

Figure 6: Storage shear modulus G' (in Pa) versus temperature T (in K), for the pure matrix

and 5 vol.% CNT, at 0.1 Hz (curves "G’ pure" and "G’exp (5 %)", respectively). Two

calculated curves (G’ HK 300 nm and G’ HK 1000 nm) obtained using the HK equation with

rods of 300 nm and 1000 nm in length, respectively, are also displayed.

Calculated curves are also shown in Figure 6. They were obtained using the HK equation, on

the basis of the following statements:

(i) CNTs are assumed to be purely elastic (no viscous components) with elastic

constants independent from temperature;

(ii) The HK equation is accounting for the complex modulus of the matrix, even though

for sake of simplicity, only the storage modulus is displayed;

(iii) To obtain such calculated curves, the HK equation provides the complex modulus

from every experimental value of the pure matrix behavior obtained at increasing

temperatures. The choice of the various CNT elastic constants comes from data in

the literature, but it is worthy to notice that because CNTs are much stiffer than the

matrix (especially for their longitudinal modulus) the result does almost not

depend anymore on the exact value. Thus the chosen values were, = 100 GPa,

E

f 11

E

f 11

18

= 10 GPa, = 0.49 in the rubbery region, = 0.3, l = e = 22 nm

(corresponding to the mean CNT diameter). L is here the mean length of the CNT

straight segments.

Figure 7: Composite storage modulus G’ in function of the CNT volume fraction, calculated

with the HK equation. The black dots represent experimental data, while the curves

correspond to different CNT segment lengths L.

Figure 6 shows (i) the stiffening by CNTs calculated from the HK equation, leading to values

very close to experimental data (without any adjustable parameters) and (ii) the high sensitivity

of L, as better shown in Figure 7. However, it could be noticed that the best agreement between

simulations and the experiment on the composite containing 2 vol.% of grafted CNTs is

obtained for L=200 nm, a value significantly lower than the mean segment length measured by

electron tomography (L=590 nm). This effect might be because the CNT segments are not

ideally stiff. Moreover, CNT are not true rods, as assumed in the frame of the HK equation:

their longitudinal tensile stiffness is extremely high compared to their compressive behavior,

because of their easy buckling, which in turn decreases a lot their efficiency if their orientation

is far from the macroscopic tensile direction. When taking the measured mean segment length

E

f 22 n

m n

f

19

(L=590 nm), the calculated modulus seems to be over-estimated by less than 20 %. It is also

noteworthy that increasing the volume fraction of CNTs from 3 to 5 % does not increase the

stiffness of the composite as it should be expected. In fact, for volume fractions above the

percolation threshold, a certain amount of CNTs forms aggregates, which makes them less

effective.

The 3D analysis was performed by electron tomography on quite large but still limited volumes

(see Table 1). It is very difficult to estimate the (lack of) representativity of the 3D analysis.

Nevertheless, correlating 3D analysis and mechanical behavior simulations can give interesting

insights. Indeed, a good agreement has been found between simulations and experiments for

the same order of magnitude of the CNT segments. This suggests that the 3D analysis is fairly

representative of the whole material. However, the simulation confirms that the only way to

take benefit of such stiffening fillers is to be able to stretch them. For example, considering a

volume fraction of 2 %, the composite modulus would be of 25 GPa with segments of 200 nm,

while it would be of 180 GPa for segments of 10 m (full CNT length), i.e. one order of

magnitude higher.

4 Conclusions

The aim of this paper was to evaluate the contribution of CNTs on the mechanical behavior of

PU/CNT nanocomposites, as they are good candidates to design electrostrictive systems. The

first part of this work dealt with the quantification of the CNT dispersion and orientation states.

For this purpose, electron tomography has been performed in an Environmental Scanning

Electron Microscope in the transmission mode. Electron tomograms have been reconstructed,

segmented, and the CNT distribution quantified. For grafted CNTs within the analyzed volume,

no contact between the CNTs was found (contrarily to what was observed with ungrafted

20

CNTs). Moreover, samples containing either grafted or ungrafted CNTs exhibit similar CNT

orientations: the CNTs were found to lie in the film plane and have a preferential orientation

along the casting direction. The second part of the study focused onto the evaluation of

mechanical properties of PU, stiffened by CNTs. A model based on analytical equations,

without any adjustable parameter, was used. It is interesting to notice that, in our study, as a

very rough approximation, a CNT was be assumed to be a set of separate stiff rods of which

length was determined from tomography observations. The calculation results showed the

consistency between microstructural observations and the stiffening effect induced by CNTs. It

has been clearly shown that due to their waviness, CNT are poorly efficient as stiffening

particles at the studied concentrations. Fully stretching 10 m long nanotube would however

increase the composite modulus by almost 10 for a fraction of only 2 vol.%. More generally,

the method presented in this paper, namely the combination of 3D analysis and modeling, is a

powerful tool to understand and predict the macroscopic properties of nanocomposites.

Acknowledgements

The authors acknowledge the French Agence Nationale de la Recherche (ANR) for financial

support, under grant NAPOLECO (ANR- 2010-INTB-910-01), the Consortium Lyon Saint-

Etienne de Microscopie (clym.fr) for the access to the JEOL 2010F and FEI ESEM XL30-FEG

microscopes, and the Centre Technologique des Microstructures for the access to the cryo-

ultramicrotome.

Conflicts of interest

There are no conflicts of interest to declare.

References

21

[1] M. Watanabe, T.H., M. Suzuki, Y. Amaike Y, Electric conduction in bending

electrostriction of polyurethanes, Appl. Phys. Lett. 74 (1999) 2717-2719.

[2] L. Irusta, M. J. Fernandez-Berridi, Photooxidative behavior of segmented aliphatic

polyurethanes, Polym. Deg. & Stab. 63 (1999) 113-119.

[3] C. Putson, L.L., D. Guyomar, N. Muensit, P-J. Cottinet, L. Seveyart, B. Guiffard,

Effects of copper filler sized on the dielectric properties and the energy harvesting

capability of nonpercolated polyurethane composites, J. Appl. Phys. 109 (2011) 024104.

[4] U. Szeluga, B. Kumanek, B. Trzebicka, Synergy in hybrid polymer/nanocarbon

composites. A review, Composites Part A 73 (2015) 204-231.

[5] Z. M. Dang, L.Wang, , Y. Yin, Q. Zhang, Q.Q. Lei, Giant dielectric permittivities in

functionalized carbon-nanotube/electroactive-polymer nanocomposites, Adv. Mater. 19

(2007) 852–857.

[6] Z.M. Huang, Y.Z. Zhang, M. Kotaki, S. Ramakrishna, A review on polymer nanofibers

by electrospinning and their applications in nanocomposites, Composites Science and

Technology 63 (2003) 2223–2253.

[7] J. Zhu, J. D. Kim, H. Peng, J. L. Margrave, V. N. Khabashesku, E. V. Barrera,

Improving the dispersion and integration of single-walled carbon nanotubes in epoxy

composites through functionalization, Nano Lett. 3 (2003) 1107–1113.

[8] H. Xia, M. Song, Preparation and characterization of polyurethane grafted single-walled

carbon nanotubes and derived polyurethane nanocomposites, J. Mater. Chem. 16 (2006)

1843–1851.

[9] M.H. Gass, K.K.K. Koziol, A.H. Windle, P.A. Midgley, Four-dimensional spectral

tomography of carbonaceous nanocomposites, Nano Lett. 6 (2006) 376-379.

22

[10] J. Yu, K. Lu, E. Sourty, N. Grossiord, C.E. Koning, J. Loos, Characterization of

conductive multiwall carbon nanotube/polystyrene composites prepared by latex

technology, Carbon 45 (2007) 2897-2903.

[11] H.S. Kim, J.H. Kim, C.M. Yang, S.Y. Kim, Synergistic enhancement of thermal

conductivity in composites filled with expanded graphite and multi-walled carbon

nanotube fillers via melt-compounding based on polymerizable low-viscosity oligomer

matrix, Journal of Alloys and Compounds 690 (2017) 274-280.

[12] E.M. Campo, D. Yates, B. Berson, W. Rojas, A.D. Winter, M. Ananth, J.J. Santiago-

Aviles, E.M. Terentjev, Macromol. Mater. Eng. 8/2017, 1600479.

[13] F. Dalmas, L. Roiban, Three-dimensional Microstructural Characterization of Polymer

Nanocomposites by Electron Tomography, in Functional and Physical Properties of

Polymer Nanocomposites (eds A. Dasari and J. Njuguna), John Wiley & Sons, Ltd,

Chichester, UK (2016).

[14] B. Natarajan, N. Lachman, T. Lam, D. Jacobs, C. Long, M. Zhao, B.L. Wardle, R.

Sharma and A. Liddle, The evolution of carbon nanotube network structure in

unidirectional nanocomposites resolved by quantitative electron tomography, ACS

Nano9 (2015) 6050-6058.

[15] K. Gnanasekaran, R. Snel, G. de With, H. Friedrich, Quantitative nanoscopy: tackling

sampling limitations in (S)TEM imaging of polymers and composites, Ultramicrosc.

160 (2016) 130-139.

[16] A. Mikhalchan, T. Gspann, A. Windle, Aligned carbon nanotube-epoxy composites: the

effect of nanotube organization on strength, stiffness, and toughness, J. Mater. Sci., 51

(2016) 10005-10025.

23

[17] K. Gnanasekaran, G. de With, H. Friedrich, Quantitative analysis of connectivity and

conductivity in mesoscale multiwalled carbon nanotube networks in polymer

composites, J. Phys. Chem. C 120 (2016) 27618-27627.

[18] M. H. Jomaa, K. Masenelli-Varlot, L. Seveyrat, L. Lebrun, M.C. Dib Jawhar, E. Beyou,

J. Y. Cavaillé, Investigation of elastic, electrical and electromechanical properties of

polyurethane/grafted carbon nanotubes nanocomposites, Composites Science and

Technology 121 (2015) 1-8.

[19] H. Xia, M. Song, J. Jin, L. Chen, Poly(propylene glycol)-Grafted Multi-Walled Carbon

Nanotube Polyurethane. Macromol. Chem. Phys. 207 (2006) 1945-1952.

[20] K. Masenelli-Varlot, A. Malchère, J. Ferreira, H. Heidari Mezerji, S. Bals, C.

Messaoudi, S. Marco, Wet-STEM tomography: principles, potentialities and limitations,

Micros. and Microanal. 20 (2014) 366-375.

[21] Z. Saghi, P. A. Midgley, Electron tomography in the (S)TEM: from nanoscale

morphological analysis to 3D atomic imaging, Annual Review of Materials Research 42

(2012) 59-79.

[22] A. Bogner, G. Thollet, D. Basset, P. H. Jouneau, C. Gauthier, Wet STEM : a new

development in environmental SEM for imaging nano-objects included in a liquid

phase, Ultramicroscopy 104 (2005) 290-301.

[23] M. Maiorca, E. Hanssen, E. Kazmierczak, B. Maco, M. Kudryashev, R. Hall, H.

Quiney, L. Tilley, Improving the quality of electron tomography image volumes using

pre-reconstruction filtering, J Struct. Biol. 180 (2012) 132-42.

[24] C. Messaoudi, T. Boudier, C.O.S. Sorzano, S. Marco, TomoJ: tomography software for

three-dimensional reconstruction in transmission electron microscopy, BMC

Bioinformatics 8 (2007) 288.

24

[25] R. Gordon, G. Herman, Three-Dimensional Reconstruction from Projections: A Review

of Algorithms, International Review of Cytology 38 (1974), 111-151.

[26 ] M. Radermacher (2007) Weighted Back-projection Methods. In: Frank J. (eds) Electron

Tomography. Springer, New York, NY

[27] T. Sanders, J. D. Roehling, K. J. Batenburg, B. C. Gates, A. Katz, P. Binev, I. Arslan,

Advanced 3-D Reconstruction Algorithms for Electron Tomography, Microsc.

Microanal. 20 ( 2014), 794-795.

[28] D. Chen, B. Goris, F. Bleichrodt, H. H. Mezerji, S. Bals, K. J. Batenburg, G. With, H.

Friedrich, The properties of SIRT, TVM, and DART for 3D imaging of tubular domains

in nanocomposite thin-films and sections, Ultramicroscopy147 (2014), 137–148.

[29] I. Arganda-Carreras, V. Kaynig, C. Rueden, K. W Eliceiri, J. Schindelin, A. Cardona, H.

S. Seung, Trainable Weka Segmentation: a machine learning tool for microscopy pixel

classification, Bioinformatics, 33 (15) (2017), 2424–2426.

[30 ] E. H. W. Meijering, W. J. Niessen, M. A. Viergever, Quantitative Evaluation of

onvolution-Based Methods for Medical Image Interpolation, Medical Image Analysis, 5

(2001), 111-12.

[31] A. Fedorov, R. Beichel, J. Kalpathy-Cramer, J. Finet, J. C. Fillion-Robin, S. Pujol,

C.Bauer, D. Jennings, F. Fennessy, M. Sonka, J. Buatti, S. Aylward, J.V. Miller, S.

Pieper, R. Kikinis, 3D Slicer as an Image Computing Platform for the Quantitative

Imaging Network, Magn Reson Imaging. 30(9) (2010), 1323–1341.

[32] C. Ma, W. Zhang, Y. Zhu, L. Ji, R. Zhang, N. Koratkar, J. Liang, Alignment and

dispersion of functionalized carbon nanotubes in polymer composites induced by an

electric field, Carbon 46 (2008), 706-720.

[33] X.L. Xie, Y.W. Mai, X.P. Zhou, Dispersion and alignment of carbon nanotubes in

polymer matrix : a review, Mater. Sci. Eng. R49 (2005) 89-112.

25

[34] E.H. Kerner, The elastic and thermo-elastic properties of composite media, Proc. Phys.

Soc. B69 (1956) 808.

[35] R. A. Dickie Interpretation of the dynamic mechanical response of heterogeneous

polymer blends in terms of continuum models, Polym. Eng. Science 19 (1979) 1042-

1045.

[36] J.C. Halpin, Environmental Factors in Composite Materials Design 1967, AFML

TR 67-423.

[37] J. C. Halpin, J. L. Kardos, Moduli of crystalline polymers employing composite theory,

J. Appl. Phys. 43 (1972) 2235.

[38] J. Pascual, F. Peris, T. Boronat, O. Fenollar, R. Balart, Study of the effects of multi-

walled carbon nanotubes on mechanical performance and thermal stability of

polypropylene, Polym. Engin. Sci 52 (2012) 733-740.

[39] C. W. M. Bastiaansen, P. J. R. Leblans, P. Smith, The Theoretical Modulus of Biaxially

Oriented Polymer-Films, Macromolecules 23 (1990) 2365-2370.

[40] J. Yu, H. K. Choi, H.S. Kim, S.Y. Kim, Synergistic effect of hybrid graphene

nanoplatelet and multi-walled carbon nanotube fillers on the thermal conductivity of

polymer composites and theoretical modeling of the synergistic effect, Composites Part

A 88 (2016) 79-85.

[41] J.N. Coleman, U. Khan, W.J. Blau, Y.K. Gun’ko, Small but strong: a review of the

mechanical properties of carbon nanotube-polymer composites, Carbon 44 ( 2006)

1624-1652.

[42] Q.P. Feng, X.J. Shen, J.P. Yang, S.Y. Fu, Y.W. Mai, K. Friedrich, Synthesis of epoxy

composites with high carbon nanotube loading and effects of tubular and wavy

morphology on composite strength and modulus, Polymer 52 (2011) 6037-6045.

26

[43] R. Arasteh, M. Omidi, A.H.A. Rousta, H. Kazerooni, A study on effect of waviness on

mechanical properties of multi-walled carbon nanotube/epoxy composites using

modified Halpin-Tsai theory, J. Macromol. Sci. Part B Phys. 50 (2011) 2464-2480.

[44] M.K. Yeh, N.H. Tai, J.H. Liu, Mechanical behavior of phenolic-based composites

reinforced with multi-walled carbon nanotubes, Carbon 44 (2006) 1-9.

[45] Y. Brechet, J.Y. Cavaillé, E Chabert, L. Chazeau, R. Dendievel, L. Flandin, C. Gauthier,

Polymer based nanocomposites : effects of filler-filler and filler-matrix interactions,

Adv. Eng. Mat. 3 (2001) 571-577.

[46] V. Favier, H. Chanzy, J.Y. Cavaillé, Polymer nanocomposites reinforced by cellulose

whiskers, Macromol. 28 (1995) 6365-6367.

[47] S. Etienne, J.Y. Cavaillé, J. Perez, R. Point ,M. Salvia, Automatic system for analysis of

micromechanical properties, Rev. Sci. Instrum. 53 (1982) 1261.